1. Field of the Invention
The present invention relates to holographic optical processing apparatus and methods, and particularly to those apparatus and methods relating to multiplexing and fixing and erasing volume holograms in photorefractive media and optical second harmonic generation in photorefractive media by optically induced periodic poling.
2. Description of the Prior Art
An optical hologram is a record of the interference pattern produced when two wavefronts of light overlap. These wavefronts must be mutually coherent so that the interference pattern is stationary in space during the recording process. Mutual coherence merely means that there is a fixed phase relationship between the spatially overlapping parts of the two wavefronts.
In the normal practice of recording a hologram, the two wavefronts are derived from a single sufficiently coherent light source by means of a beam splitting device. One of these two beams is the reference beam, and the other beam carries the information, and is otherwise known as the signal beam. The reference beam, once superimposed with the signal wavefront, acts as a phase reference standard. The two wavefronts interfere, and the interference shows up as a pattern of light and dark. The recorded interference patterns each constitute an ensemble of diffraction gratings that are capable of constructively diffracting properly directed illuminating light to reconstruct an image of the recorded subject. This interference pattern can be recorded by placing a piece of photosensitive material in the original space where the two wavefronts overlap and interfere. This process is known as recording a hologram, which therefore means storing a phase or amplitude pattern which includes the information.
During the reconstruction (or data retrieval) process, only the reference beam is present, and it passes through the developed hologram as it did during the recording period. The beam is now phase and/or amplitude modulated by the holographic pattern previously recorded there. The hologram impresses on the wavefront the same interference pattern which existed during recording of the hologram. When this pattern has been impressed, the reference wavefront produces a set of waves with the proper phase delays, which add constructively in phase to form a replica of the signal beam used during recording. The signal beam is therefore said to have been reconstructed.
As a technique, optical holography shows great promise for a number of possible applications, most notably as a memory function; information could be stored by being recorded in a hologram, and retrieved by reading out the hologram.
For such possible applications, it is usually desirable to multiplex many holograms in the same medium. This would mean recording several superimposed holograms within the medium (which is also known as multiplexing them). In such applications, each such hologram is known in the art as a picture or a page. There are two difficulties in this endeavor. The first one is the limited capacity of holographic materials, and the second is with individually addressing each hologram without interference from the other coexisting holograms when reading it out (also known as demultiplexing).
A dramatic advantage in both directions is offered by shifting from thin photographic materials to thick holographic materials, which allow volume holograms to be recorded in them. Bulk photorefractive crystals store volume holograms as modulations of the underlying refractive index of the material.
Thick photosensitive materials are capable of storing far more data than thin materials. (P. J. Van Heerden, Applied Optics vol. 2, no. 4, April 1963, pp. 393-400.) Another advantage of volume holograms over those in photographic media is that there is no developing of the medium required. Sometimes thermal or electrical fixing is a recommended process, but not necessary. Furthermore, thick materials are reusable, being erasable electrically (F. Micheron, C. Mayeux, and J. C. Trotier, Applied Optics vol. 13, no. 4, April 1974, pp. 784-787), optically (G. T. Kavounas and W. H. Steier, Topical Meeting On Photorefractive Materials, Effects, and Devices, Technical Digest Series Volume 17, August 12-14, 1987, Los Angeles, Calif.) or thermally (J. J. Amodei, D. L. Staebler, Appl. Phys. Lett. 18, 540-545, 1971), without necessarily changing the apparatus.
A crystal is ferroelectric if a spontaneous polarization can be induced in it by applying an electric field, and additionally if this spontaneous polarization can be reversed by applying the same electric field in the opposite direction. A subgroup of non-centrosymmetric crystals exhibit photorefractivity, an effect that is commonly used to store volume phase holograms. Two coherent, monochromatic laser beams interfering in a photorefractive crystal will induce an electronic space charge field with the same periodicity as the optical interference pattern, through the photorefractive effect. This electronic space charge field may be of the order of 1 kV/cm. Bulk photorefractive crystals have been used for applications such as data storage, defect enhancement, optical correlation and convolution, optical interconnects, associative memories, etc. (Hesselink et al., U.S. Pat. No. 4,927,220) These applications have used mostly commercially available bulk crystals such as the piezoelectrics LiNbO.sub.3 (Lithium niobate), SBN (Strontium Barium niobate), KLTN (Potassium Lithium Tantalum Niobate) and the paraelectric BSO (Bismuth Silicon oxide) (J. B. Thaxter and M. Kestigian, Applied Optics vol. 13, no. 4, April 1974, pp. 913-924). Volume holograms have also been written in materials containing living cells, algae, and organic crystals such as nonlinear polymers, e.g. NPDA (Bisphenol-A-diglycidylether 4-Nitro-1,2-phenylenediamine).
SBN is a medium of particular interest. It has a composition Sr.sub.x Ba.sub.1-x Nb.sub.2 O.sub.6, with x typically having values in the range of 0.25 and 0.75. As x tends to 0.75, the electrooptic coefficient increases in magnitude, accordingly increasing the available electrooptic effect and hologram diffraction efficiency.
It is also well known that the hologram capacity or minimum diffraction efficiency increases when an electric field is applied to the photorefractive medium. Specifically, Thaxter in U.S. Pat. No. 3,652,145 has shown that the read out diffraction efficiency of a photorefractive hologram stored in a single SBN crystal depends strongly on a uniform electric field applied along the z axis.
Multiplexing Holograms PA0 a) Holograms overlapping within the material PA0 1) Pure angle multiplexing and demultiplexing PA0 2) Pure wavelength multiplexing and demultiplexing PA0 3) Hybrid multiplexing and demultiplexing PA0 b) Holograms not overlapping within the material PA0 Fixing Holograms PA0 Selective Erasure of Portions of a Hologram PA0 Second Harmonic Generation and Parametric Amplification PA0 Multiplexing PA0 a) Electric field multiplexing of holograms PA0 b) Mechanical stress multiplexing of holograms PA0 c) Temperature multiplexing of holograms PA0 d) Hybrid multiplexing--demultiplexing. PA0 Fixing PA0 Selective Erasing of Portions of Holograms PA0 Second Harmonic Generation by Optically Induced Periodic Poling
The problem of recording and then individually addressing each recorded hologram is presently tackled in a number of ways.
This method corresponds to the storage of an ensemble of holographic pages, each page distributed over and sharing the volume of the material.
A common method to individually address a single page out of an ensemble is by angularly multiplexing the holograms in the medium, which means that each hologram is recorded at a different angle of incidence of the writing beams. (J. E. Ford, J. Ma, Y. Fainman, and S. H. Lee, Y. Taketomi, d. Bize and R. R. Neurgaonkar, J. Opt. Soc. Am. Vol. 9, no. 7, July 1992, pp. 1183-1192) Each hologram can be individually addressed by having the reference beam impinge at the angle of incidence that the hologram was written at. The disadvantage of this method is that it requires either a moving mirror or acoustooptic or electrooptic beam deflectors to change the angles of incidence. In general it suffers from relatively large crosstalk relative to wavelength multiplexing.
Another way of multiplexing volume holograms in a single medium is by recording the holograms at different wavelengths. (G. A. Rakuljic, V. Leyva and A. Yariv, Optics Letters vol. 17, no. 20, Oct. 15, 1992, pp. 1471-1473) The advantage of this method is that a single, multi-chromatic source, such as a dye laser, may be used to record and then read out different holograms without changing the angles of incidence. A disadvantage is that the diffraction efficiency of each hologram varies with the wavelength. Another disadvantage is that tunable laser sources with light power exceeding 100 mW are complex, costly devices.
Additionally, there are hybrid approaches. Holograms that have been recorded by wavelength multiplexing can be read out by angle demultiplexing, and conversely, holograms that have been recorded by angle multiplexing can be read out by wavelength demultiplexing. A general problem with hybrid approaches is that they result in spatial distortion of the reconstructed signal beam.
Naturally, with hybrid multiplexing, the reconstructed signal beam will contain the phase information of the recording signal beam, but will not be necessarily of the same wavelength.
Another approach is by space division multiplexing of the holograms. The holographic recording medium is considered divided into many pixels and one hologram is recorded in each pixel. Complex apparatus is required to steer the reading beam to the requisite pixel, which usually involves either a moving mirror or acoustooptic or electrooptic beam deflectors.
When volume holograms have first been written in a photorefractive material, they are called "dynamic" electronic holograms, dynamic in the sense that they inevitaby decay when being read out by a reference beam. In other words, the diffraction efficiency of the hologram is reduced with readout time. The time constant of such decay is relatively close (i.e. within an order of magnitude) to the time constant of writing the hologram, if the readout reference beam is of the same wavelength, intensity and angle as the writing beams. This problem may be avoided by reconstruction with a readout beam substantially weaker than the writing beam. One technique for extending the readout life of dynamic holograms is to read and write with different polarizations, called enhanced non destructive readout.
Another way of dealing with this decay problem is by a process of "fixing" the holograms. The term has its origin from the equivalent art of fixing photographic materials.
A convenient way of defining a "fixed" hologram would be a hologram that has a decay time constant that is substantially larger than its recording time. The ratio is typically many orders of magnitude, but it can be as low as one order of magnitude. The decay time constant in this instance would be that of the decaying hologram, as it is being read out with a light beam of the same wavelength, intensity and angle as was used in recording it. This would not necessarily be a practical way to read out a hologram (because writing intensities are generally much larger than readout intensities), but is a good way of defining the term "fixed hologram".
Permanent fixing of volume holograms in photorefractive media was first demonstrated in LiNbO.sub.3 using a thermal fixing process (Amodei, J. J. and Staebler, D. L.: `Holographic Pattern Fixing in Electro-optic Crystals`, Appl. Phys. Lett., 1971, 18, pp. 540-542). A hologram would be fixed when the time constant of its decay (caused by readout) is much larger (many orders of magnitude) than the time constant involved in writing it. The physical mechanism responsible for the fixed grating is believed to be either ionic compensation of the space charge grating during a thermal development cycle (Matull, R. and Rupp, R. A.: `Microphotometric investigation of fixed holograms`, J Phys. D: Appl. Phys., 1988, 21, pp. 1556-1565), or space charge induced local ferroelectric domain reversal (Kovalevich, V. I., Shuvalov, L. A., and Volk, T. R.; `Spontaneous Polarization Reversal and Photorefractive Effect in Single-Domain Iron-Doped Lithium Niobate Crystals`, Phys. Stat. Sol. (a), 1978, 45, pp. 249-252).
Permanent fixing was soon thereafter reported in SBN:75, using an electrical fixing pulse to bias the hologram about the coercive field (Micheron F. and Bismuth, G.: `Field and time threshold for the electrical fixation of holograms recorded in Sr.sub.0.75 Ba.sub.0.25 Nb.sub.2 O.sub.6 crystals`, Appl. Phys. Lett., 1973, 23, pp. 71-72), or photoinduced ferroelectric domain nucleation upon cooling from the paraelectric phase (Micheron F. and Trotier, G. C.: `Photoinduced Phase Transitions in (Sr,Ba)Nb.sub.2 O.sub.6 Crystals and Applications`, Ferroelectrics, 1974, 8, pp. 441-442). The electrical fixing technique was also applied to BaTiO.sub.3 (Micheron F. and Bismuth, G.: `Electrical Control of Fixation and Erasure of Holographic Patterns in Ferroelectric Materials`, Appl. Phys. Lett. 1972, 20, pp. 79-81).
In addition, fixing has been reported in BTO (McCahon, S. W., Rytz, D., Valley, G. C., Klein, M. B., and Wechsler, B. A.: `Hologram fixing in Bi.sub.12 TiO.sub.20 using heating and an ac electric field`, Appl. Opt., 1967, 28, pp. 1967-1969), BSO (Herriau, J. P. and Huignard, J. P.: `Hologram fixing process at room temperature in photorefractive Bi.sub.12 SiO.sub.20 crystals`, Appl Phys Lett , 1986, 49, pp. 1140-1142), and KTN (Leyva, V. Agranat, A. and Yariv, A.: `Fixing of a photorefractive grating in KTa.sub.1-x Nb.sub.x O.sub.3 by cooling through the ferroelectric phase transition`, Opt Lett., 1991, 16, pp. 554-556).
A common characteristic of all these fixing techniques is a single process step of development in which all the previously recorded space charge holograms are simultaneously fixed. This would involve, for example, heating a LiNbO.sub.3 memory to 130.degree. C., or applying an electrical pulse. After the development process step, the holographic memory is unable to be selectively updated. To update a single page of holographic data, the entire memory (i.e. all pages) must be erased and then rewritten. This would involve, for example, heating a LiNbO.sub.3 memory to 200.degree. C., or .gamma.-irradiating it. For applications such as a random access memory, the ability to selectively update existing fixed holograms is highly desirable.
It would be very desirable to update only portions of a permanently recorded hologram. The prior art has not achieved this yet.
Second Harmonic Generation (SHG) and Parametric Amplification are well known in the art, and described in many text books. They usually depend on the crystal being naturally anisotropic, or specially grown to have some periodicity of ferroelectric domain built in. Alternately, angle phase matching is required for SHG to occur.
A compact blue or green coherent light source is essential for high-density optical data storage, laser printing, and display applications. Laser-diode-based second-harmonic generation (SHG) devices are potentially useful for compact blue or green coherent light sources. The conversion efficiency of quasi-phase matched (QPM) SHG is highest when periodic reversal of the sign of the nonlinear coefficient d of the material occurs in the phase matching period. [J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1981 (1962). S. Somekh and A. Yariv, Opt. Commun. 6, 301 (1979).] LiNbO.sub.3 can realize efficient SHG devices on account of its large nonlinear optical coefficient d.sub.33. A variety of methods of domain inversion of LiNbO.sub.3 have been reported [E. Lim, M. M. Fejer, and R. L. Byer, Electron. Lett. 25, 174 (1989). J. Webjorn, F. Laurell, and G. Arvidson, IEEE Photon. Technol. Lett. 1, 316 (1989).], but these methods cannot be used to fabricate a sufficiently fine and deep periodically inverted domain structure.
A fine and deep domain in LiNbO.sub.3 has been fabricated by applying an external field. [M. Yamada, N. Nada, and K. Watanabe, Integ. Photon. Res. Tech. Dig. 10, TuC 2 (1992)] A periodically inverted domain structure in a LiNbO.sub.3 substrate by applying an external electric field, which yields an efficient first-order QPM-SHG device has also been fabricated. [M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993)]. The problem is that the modulation depth of the grating will decrease with distance from the surface on which the special electrod has been applied. Further, the alternating period seems limited by the electrode spacing. For manufacturing purposes it seems limited to a few microns.
It has been reported in the literature that the domain inversion of LiNbO.sub.3 is difficult at room temperature. [H. D. Megaw, Acta Cryst. 7, 187 (1954).] LiNbO.sub.3 is usually broken without domain inversion when an external field is applied at room temperature. The external field for domain inversion of LiNbO.sub.3 is close to that of the electron avalanche, so the LiNbO.sub.3 substrate is broken without its spontaneous polarization being inverted with the application of an external field.
Quasi-phase-matched (QPM) [J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1981 (1962).], efficient second-harmonic generation (SHG) using periodic reversals in the sign of the nonlinear coefficient to compensate for dispersion has recently been demonstrated in bulk [D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, in Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), p. 614, postdeadline paper CPDP22.] as well as in waveguide devices. [K. Yamamoto, K. Mizuuchi, and T. Taniuchi, Digest of Conference on Lasers and Electro-Optics (Optical Society of America, Washington, D.C., 1991), p. 616, postdeadline paper CPDP23. C. J. van der Poel, J. D. Bierlein, J. B. Brown, and S. Colak, Appl. Phys. Lett. 57, 2074 (1990).] QPM allows interactions between waves polarized such that the nonlinearity is maximized and allows interactions in materials for which birefrigent phase matching is not possible, e.g., SHG of blue light in LiNbO.sub.3. First-order QPM requires sign reversals of the effective nonlinear coefficient with a period equal to two coherence lengths. Alternating ferroelectric domains have been a achieved in LiNbO.sub.3, LiTaO.sub.3, and KTiOPO.sub.4 (KTP) by modulating the dopant concentration during growth [Nai-Ben Ming, Jing-Fen Hong, and Duan Feng, J. Mater. Sci. 17, 1663, (1982)], indiffusing dopants [C. J. van der Poel, J. D. Bierlein, J. B. Brown, and S. Colak, Appl. Phys. Lett. 57, 2074 (1990); E. J. Lim, M. M. Fejer, and R. L. Byer, Electron. Lett. 25 174 (1989).], applying electric fields [A. Feisst and P. Koidl, Appl. Phys. Lett. 47, 1125 (1985); S. Matsumoto, E. J. Lim, M. M. Fejer, and H. M. Hertz, Digest of Integrated Photonics Research Topical Meeting (Optical Society of America, Washington, D.C., 1991), p. 79, paper ThC4] or by techniques using electron beams [H. Ito, C. Takyu, and H. Inaba, Electron. Lett. 27, 1221 (1991)] or SiO.sub.2 masks [J. Webjorn, F. Laurell, and G. Arvidsson, IEEE Photon. Technol. Lett. 1, 316 (1989); M. Fujimura, T. Suhara, and H. Nishihara, Electron. Lett. 27, 1207 (1991)].
In LiNbO.sub.3 QPM allows nonlinear interactions between waves polarized along the z axis, for which the largest nonlinear coefficient d.sub.eff =2d.sub.33 /.pi.=20.9 pm/V can be used. [Landolt-Bornstein, in Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, Neue Serie, edited by K. -H. Hellwege and A. M. Hellwege (Springer, Berlin, 1975); R. C. Eckhardt, H. Masuda, Y. X. Fan, and R. L. Byer, IEEE J. Quantm Electron. 26, 922 (1990).] In practice, the creation of the required, finely spaced domains with sufficiently accurate periodicity is a challenging task. [M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer (unpublished). ] Feng, et al. produced Czochralski-grown LiNbO.sub.3 crystals doped with 0.5-1 wt. % Yttrium with domain lengths of 3.4 .mu.m to frequency double the 1.064 .mu.m Nd:YAG laser line. [D. Feng, N. B. Ming, J. F. Hong, Y. S. Yang, J. S. Zhu, Z. Yang, and Y. N. Wang, Appl. Phys. Lett. 37, 607 (1980); Y. H. Xue, N. B. Ming, J. S. Zhu, and D. Feng, Chin. Phys. 4, 554 (1984).] The observed conversion efficiency increased quadratically with the crystal length as expected for perfect domain periodicity up to lengths of about 680 .mu.m, corresponding to 200 domains. For longer crystals the increase was linear, revealing domain-boundary position errors on the order of the coherence length. These positions errors are probably caused by variations in growth speed due to thermal fluctuations during the Czochralski growth.
The laser-heated pedestal growth method [M. M. Fejer, J. L. Nightingale, G. A. Magel, and R. L. Byer, Rev. Sci Instrum. 55, 1791 (1984)] is another method for achieving periodic poling for QPM at room temperature for frequency doubling [D. H. Jundt, G. A. Magel, M. M. Fejer, and R. L. Byer, Appl. Phy. Lett. 59, 2657 (1991)].
Materials with high nonlinearity, good optical quality, and the ability to phase match for direct frequency doubling of GaAlAs diode lasers are in demand for the development of compact sources of short-wavelength light to be used in optical storage and other applications. Lithium niobate (LiNbO.sub.3) has insufficient biregringence to use conventional phase-matching techniques at these wavelengths. The capability of growing periodic ferroelectric domain structures of high spatial frequency in LiNbO.sub.3 was demonstrated [G. A. Magel, M. M. Fejer, and R. L. Byer, Appl. Phy. Lett. 56, 108 (1990)].
Some technique to maintain the relative phase between the interacting waves must be employed to obtain efficient conversion in optical second harmonic generation and other nonlinear optical processes. Quasi-phase matching (QPM) was devised independently by Bloembergen, et al. [J. A. Armstrong, N. Bloembergen, J Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev., vol 127, pp. 1918-1939, 1962.] and Franken and Ward [P. A. Franken and J. F. Ward, "Optical harmonics and nonlinear phenomena," Rev. Mod. Phys., vol. 35, pp. 23-39, 1963.] for this purpose. This invention, which actually predates the development of birefrigent phase-matching, corrects the relative phase at regular intervals by means of a structural periodicity built into the nonlinear medium. A particularly effective type of periodic structure is one in which the sign or magnitude of the nonlinear coefficient is modulated throughout the material.
Several experimental demonstrations of quasi-phase-matched optical second-harmonic generation (SHG) have been made. It was recognized early that multidomain ferroelectric crystals could show an enhancement of SHG. [R. C. Miller, "Optical harmonic generation in single crystal BaTiO.sub.3," Phys. Rev., vol. 134, pp. Al313-Al319, 1964.]. Rotationally twinned crystals of ZnSe, ZnS, and other materials were considered for the enhancement of SHG by several researchers in the early 1970s. [J. Muzart, F. Bellon, C. A. Arguello, and R. C. C. Leite, "Generation de second harmonique non colineaire et colineaire dans ZnS accord de phase (`phase matching`) par la structure lamellaire du cristal," Opt. Commun., vol. 6, pp. 329-332, 1972; C. F. Dewey, Jr., and L. O. Hocker, "Enhanced nonlinear optical effects in rotationally twinned crystal," Appl. Phys. Lett., vol. 26, pp. 442-444, 1975; L. O. Hocker and C. F. Dewey, Jr., "Enhancement of second-harmonic generation in zinc selenide by crystal defects," Appl. Phys. Lett., vol. 28, pp. 267-270, 1976] Levine, et al. [B. F. Levine, C. G. Bethea, and R. A. Logan, "Phase-matched second harmonic generation in a liquid-filled waveguide," Appl. Phys. Lett., vol. 26, pp. 375-377, 1975] applied a periodic electric field to liquid nitro-benzene to modulate its nonlinear susceptibility for phase matching. Alternating stacks of thin plates of CdTe [M. S. Piltch, C. D. Cantrell, and R. C. Sze, "Infrared second-harmonic generation of nonbirefringent cadmium telluride," J. Appl. Phys., vol. 47, pp. 3514-3517, 1976 (5 plates, m=5)], GaAs [A. Szilagyi, A. Hordvik, and H. Schlossberg, "A quasi-phase-matching technique for efficient optical mixing and frequency doubling," J. Appl. Phys., vol. 47, pp. 2025-2032, 1976 (2-5 plates, m=3)], [D. E. Thompson, J. D. McMullen, and D. B. Anderson, "Second-harmonic generation in GaAs `stack of plates` using high-power CO.sub.2 laser radiation," Appl. Phys. Lett., vol. 29, pp. 113-115, 1976 (1-12 plates, m=1)], quartz [M. Okada, K. Takizawa, and S. Ieiri, "Second harmonic generation by periodic laminar structure of nonlinear optical crystal," Opt. Commun., vol. 18, pp. 331-334, 1976 (up to 24 quartz laminae, and 6 LiNbO.sub.3 laminae, all with large m)], and LiNbO.sub.3 [M. Okada, K. Takizawa, and S. Ieiri, "Second harmonic generation by periodic laminar structure of nonlinear optical crystal," Opt. Commun., vol. 18, pp. 331-334, 1976 (up to 24 quartz laminae, and 6 LiNbO.sub.3 laminae, all with large m).] were constructed by several researchers for QPM SHG experiments. In recent years, LiNbO.sub.3 [Y. H. Xue, N. B. Ming, Z. S. Zhu, and D. Feng, "The second harmonic generation in LiNbO.sub.3 crystals with period laminar ferroelectric domains," Chinese Phys., vol. 4, pp. 554-564, 1984.; A. Feisst and P. Koidl, "Current induced periodic ferroelectric domain structures in LiNbO.sub.3 applied for efficient nonlinear optical frequency mixing," Appl Phys. Lett., vol. 47, pp. 1125-1127, 1985] and LiTaO.sub.3 crystals [ W. S. Wang, Q. Zhou, Z. H. Geng, and D. Feng, "Study of LiTaO.sub.3 crystals grown with a modulated structure: I. Second harmonic generation in LiTaO.sub.3 crystals with periodic laminar ferroelectric domains," J. Cryst. Growth, vol. 79, pp. 706-709, 1986] and single-crystal fibers [G. A. Magel, M. M. Fejer, and R. L. Byer, "Quasi-phase-matched harmonic generation of blue light in periodically poled LiNbO.sub.3," Appl. Phys. Lett., vol. 56, pp. 108-110, 1990] having periodically alternating ferroelectric domain structures have been grown for application to QPM SHG. It has also been suggested that QPM may account for the surprisingly high SHG efficiencies sometimes observed in glass fibers [F. C. Farries, P. St. J. Russel, M. E. Fermann, and D. N. Payne, "Second-harmonic generation in an optical fiber by self written .chi..sup.(2) grating," Electron. Lett., vol. 23, pp. 322-324, 1987; R. H. Stolen and H. W. K. Tom, "Self-organized phase-matched harmonic generation in optical fibers," Opt. Lett., vol 12, pp. 585-587, 1987], and, in fact, periodic electric fields have been intentionally applied to enhance SHG in silica fibers [R. Kashyap, "Phase-matched period electric-field-induced second-harmonic generation in optical fibers," J. Opt. Soc. Amer. B, vol. 6, pp. 313-328 1989].